Inductive Reactance (X_L)
Enter L and frequency (or solve for either) to get reactance, impedance, phase and current.
Step-by-step
- Enter valid values to begin.
Ideal inductance in series with a constant resistance R, sinusoidal steady state, rms values. The series model ignores core saturation, skin effect, core loss and winding capacitance, so it is valid well below the self-resonant frequency. Only the fields needed for the chosen mode are validated. If V is 0, current and power are skipped. The Q factor shown is XL/R of this series model.
Inductive Reactance: Opposition That Grows With Frequency
Core Engineering Principles
Resistance burns power; reactance stores it and hands it back every cycle. An inductor resists a change in current, so the faster the current tries to swing, the harder it pushes back, and XL = 2πfL rises in a straight line with frequency. At DC the coil is just its wire. At 1 kHz a 10 mH choke is already 63 Ω. We never add reactance and resistance directly, because they sit 90° apart: |Z| = √(R² + XL²), with a phase angle of atan(XL/R).
This one relation is behind line reactors that tame drive harmonics, chokes that block switching noise, ballasts that limit lamp current without dissipating it, and the L in every LC filter. But the formula describes an ideal part, and real coils stop obeying it. Skin effect raises resistance at high frequency, and winding capacitance forms a self-resonant frequency (SRF). Above SRF the part looks capacitive and your “choke” passes the noise you meant to block. We stay well under SRF and under the saturation current, because a saturated core collapses L and reactance falls with it.
|Z| = √(R² + XL²) • θ = atan(XL/R) • I = V / |Z|
Q (var) = I² XL • Q factor = XL / R
NEC & Standard References
IEC 60050-131 (International Electrotechnical Vocabulary, circuit theory) defines reactance, impedance and phase angle, and IEEE 100 gives the matching dictionary entries. IEC 60076-6 covers reactors used in power systems, including their rating and loss. IEC 62024-1 specifies high-frequency inductors for electronics, including inductance, rated current and self-resonant frequency measurement. These documents define terms and tests; the datasheet sets the limits. Check the adopted edition.1. ω = 2π × 1000 = 6283.2 rad/s, so XL = 6283.2 × 0.010 = 62.83 Ω.
2. |Z| = √(5² + 62.83²) = 63.03 Ω.
3. θ = atan(62.83 / 5) = 85.45°, nearly pure inductive.
4. I = 120 / 63.03 = 1.904 A.
5. Voltage across L = 1.904 × 62.83 = 119.6 V; across R = 9.52 V.
6. Reactive power Q = 1.904² × 62.83 = 227.7 var; Q factor = 62.83 / 5 = 12.57.
Real power is only 18.1 W, which is the winding heat.
- Don’t trust L above SRF. Past self-resonance the part is a capacitor, so read the impedance curve.
- Remember ESR heating. Reactance does not dissipate power, but the series resistance does; I²R can run a choke hot even when the volt-amperes look modest.
- Respect DC saturation. Bias or fault current beyond the rated saturation current drops L sharply, so reactance collapses and current spikes.
- Never mix ω and f. Putting ω = 2πf into a formula that already contains 2π gives an answer 6.28 times too large.
- Allow for tolerance. Inductors are commonly ±10% to ±20%, and XL moves by the same amount, so design for the worst case.